The Constitution says that direct taxes (taxes on property and person) must be apportioned among the states (divided based on the last census). The income tax is not so apportioned. Therefore it must be an indirect tax (a tax on an activity or event). There is no third kind of tax, contrary to what some have claimed.
"...the...complete and plenary power of income taxation possessed by Congress from the beginning [cannot be] taken out of the category of indirect taxation to which it inherently belong[s]." (Stanton v. Baltic Mining Co., 240 U.S. 103) (1916)
"A tax laid upon the happening of an event, as distinguished from its tangible fruits, is an indirect tax.." (Tyler v. U.S., 281 U.S. 497) (1930)
So the subject of the tax must be the activity or event that produced the income, not the income itself. A legislative draftsman said it most clearly:
"The income tax is, therefore, not a tax on income as such. It is an excise tax [a type of indirect tax] with respect to certain activities and privileges which is measured by reference to the income which they produce. The income is not the subject of the tax: it is the basis for determining the amount of tax." (F. Morse Hubbard, Treasury Department legislative draftsman. House Congressional Record March 27th 1943, page 2580.)
So income is used to compute the tax, but it is not the subject of the tax. This turns out to be very important.
Note the use of the word 'privileges'. We will come back to it.